At last! The House of Commons public administration select committee yesterday called for a top pay commission. About time, you might think, to restrain out-of-control salaries that rocket-propel national inequality. The new commission would issue top pay guidelines, naming and shaming organisations that can't justify excessive salaries. Good.

Except it leaves a great gaping hole. This top pay commission would only cover the public sector, not the private sector where the problem originates. The report rightly castigates pay that turns chief executives of some local authorities, housing associations, universities, quangos, or the BBC director general into public-sector nabobs of extravagant excess. But the public service is not an isolation zone. It cannot avoid "the contagion effect" of the outside world, as the LSE's Tony Travers warned the committee. The report reminds us: "Those at the top of the public sector continue to earn much less than those at the top of the private sector." Just so. One sector can't be tackled without reining in the other.

The line dividing private from public has become blurred, with some services hived off into independent trusts, duties devolved to quangos and markets introduced to ginger things up. Companies win public contracts by stealing the expertise of public managers. Mega-pay tempts some away – so how is the public sector to hold on to them?

There should be special honour in public service, with knighthoods and medals reserved for public heroes, not squandered on the likes of Sir Fred Goodwin. If parliament and people revered their servants, they might accept lower pay. Good people might feel honoured by recent Essex university research showing "the nicer you are the worse you are likely to be paid". But instead, public managers are told – against the evidence – that private managers are more dynamic and efficient. Odd how this myth persists despite the banking scandal, BA's dispute and Eurostar chaos. If the public sector asked you to stay in all day to wait for repairmen and parcels, there would be outrage. Yet ministers often join the Taxpayers' Alliance in fuelling contempt for all things public.

Public jobs are tough. Running a local authority, or a beacon comprehensive or teaching hospital in a hard-pressed borough, takes more managerial talent than running any company. Selling food or cars has just one target – the bottom line. Compare that with a public manager's multiple goals. A happy and well-educated child or a recovered hip-fracture patient returned safely to their home require skills no investment banker has. That is why it's one-way traffic: no one asks retail managers to run schools, hospitals or councils. They might find the responsibility for other people's lives hair-raising – and the pay would be too low. However, public servants jeopardise the respect they deserve once they, too, want their worth weighed in gold.

That is why, as Compass proposes, we need a high pay commission covering both sectors. To be fair to the public administration committee's excellent report, it was beyond their remit to include the private sector. As committee chair Tony Wright points out, their proposed commission would track private sector comparators and report on general pay trends: "There is no doubt that private pay drags the public sector along in its wake."

A YouGov poll for Compass shows two thirds of voters want a high pay commission. Worsening inequality causes concern, even to the Conservatives. An Institute for Fiscal Studies report this month seeks the reason why income gaps have widened so sharply. It factored in age, sex, region, education, skill and occupation. It found, unsurprisingly, that education is the big driver of the growing gap between unskilled and professional/managerial incomes. But what surprised them was that education and skill could only account for less than half the difference in pay. The IFS confessed with "some humility" that there was simply no explanation for over half the rise in pay differences.

Top people pay themselves mega-sums because they can, not because they're worth it in any way the IFS can measure or explain. Cartels are seizing the citadels and paying themselves whatever they like, untrammelled by shareholders whose interests go unguarded by pension fund managers living in the same loop. These super-earnings convert into wealth that solidifies rank from one generation to the next. The ONS's first report on distribution of the country's wealth was published the same day: 91% of wealth belongs to the top half of the population, most to the top 10%, while the bottom 10% owes more that it owns. It will go on getting worse.

Politicians live in fear of the power of money; the threat of the rich taking their business abroad freezes the marrow of a Treasury afraid of losing tax revenues – although so much top tax is avoided. How wise of the Bank of England's head of financial stability, Andy Haldane, to say their departure might be a price worth paying: he knows Switzerland and the Caymans beckon few of these paper tigers. Bloomberg yesterday reported few would go: Tiny Geneva has a housing shortage, crowded schools and a 44% income tax rate.

A report from the TUC on middle-Britain's pain makes you wonder why people have until now passively accepted the growing gap between the left-behind middle – earning around £22,000 – and the run-away rich. In the last 30 years middle incomes grew by 56% while incomes of the 90th percentile grew by 100% and the top 1% went stratospheric. A large group of workers – forklift drivers, bakers, bus drivers – saw virtually no increase. In just two decades top FTSE CEO pay soared from a multiple of 15 to 75 times the pay of their average worker.

Oddly, last week the credit rating agency Moody's warned that "social unrest" would be a credit risk in both rich and poor countries when they will be obliged (by the credit rating agencies) to make severe spending cuts. A wise government would welcome a high pay commission that set reasonable top pay guidelines to calm indignation in the austere times ahead.